Theorems · Theorem · field theory
Polynomial.natDegree_add_le_of_degree_le
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R} {n : ℕ},
p.natDegree ≤ n → q.natDegree ≤ n → (p + q).natDegree ≤ n- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- LE.le.transproof · cited by 3,151
- Polynomial.natDegreestatement and proof · cited by 1,105
- max_leproof · cited by 71
- Polynomial.natDegree_add_leproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.IsMonicOfDegree.add_rightproof · cited by 6
- Polynomial.natDegree_add_le_iff_leftproof · cited by 2
- Polynomial.add_scaleRoots_of_natDegree_eqproof · cited by 1